Elementary Mathematicians from Advanced Standpoints—A Cultural Perspective on Mathematics Education

Abstract

Many challenges face those of us for whom mathematics education research is our life's work. In some countries where significant attempts are continually being made to reform mathematics teaching, it is often a highly politicised field. While rational arguments and relevant data-gathering are valid parts of a democratic research process, awareness of the broad cultural context is paramount. Despite the challenges that adopting a new cultural perspective brings, episodes and analyses from our sociocultural research field do demonstrate much promise for advancing mathematics educational practices. In particular the relatively new ideas of values and valuing show much research promise. In this paper, referencing Felix Klein's fundamental ideas, I will analyse the twin pluralised notions of 'elementary mathematicians' and 'advanced standpoints'. In addition research focussed on a third key notion, 'pedagogical practices' will be discussed. Finally some of the implications of this three dimensional and culturally oriented research will be presented.

Values and Valuing in Mathematics Education

“…In his seminal discussion on culture and values in mathematics, Bishop (1988a) introduced six fundamental activities that he argued are universal, necessary and sufficient for the development of mathematic knowledge: counting, locating, measuring, designing, playing, and explaining. Subsequently Bishop (1988b) envisaged values as a variable of affect, and went on to describe six values that underpin the widely utilised notion of Western mathematics: rationalism and objectism; mystery and openness; control and progress.…”

“Dig Where You Stand” 7. Proceedings of the Seventh International Conference on the History of Mathematics Education. September 19-23, 2022, Mainz, Germany

“…In 2016, he was invited to Hamburg (ICME Congress) to give a talk. In this talk, Bishop suspected that Klein did not have addressed the relationship between mathematics and culture (Bishop, 2017). I was very surprised (see Tobies 1994; and decided to start my lecture at the ICHME-7 conference with Klein and culture.…”